Probability with Combinations and Permutations — Unit test Answers

A study reported that about 40% of high school students have tried out for a sport at their school. To find out if this applies to Jessica’s school, she surveyed an SRS of 20 students. Nine of them said that they had tried out for a sport. To see if this result is surprising, a simulation is to be conducted to estimate the probability of obtaining a sample result as high as this one.Let 0–3 represent students who tried out for a sport and 4–9 represent students who did not try out for a sport.

A professional pool player claims that she sinks at least one ball in a pocket on 80% of her opening break shots. In a recent set of 20 games, she sunk at least one ball on her break shot in only 14 of the games. A simulation of 100 trials was conducted to see how unusual these most recent games are.

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.What is the approximate probability that exactly one of the four characters will be a number?

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag.What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

A recent survey suggests that 47% of all televisions are connected to the internet, 32% are voice controlled, and 22% are both connected to the internet and voice controlled. Suppose a television is selected at random and it is voice controlled. What is the probability that a randomly selected voice-controlled television is also connected to the internet?

The following two-way table shows the distribution of daily traffic and weather issues in a certain large city.

A researcher randomly surveyed 1,477 farmers to determine the geographical region in which they farm and the types of crops that grow there. The two-way table displays the data.Suppose a farmer from this survey is chosen at random. Let M = farmer lives in the Midwest and V = farmer grows vegetables. What is the value of P(V|M)?

A cereal company hopes to increase its sales by putting prizes in randomly selected boxes of its lowest-selling children’s cereal. The company claims that the probability of getting a prize is 0.75.Which is the correct interpretation of this probability?

A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?

Four seniors and six juniors are competing for four places on a quiz bowl team.What is the approximate probability that all four seniors will be chosen at random?

A researcher randomly selects 95 high school students and asks their handwriting preference and how well they dance. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers writing in block letters and F = the student’s dancing skills are fair.

Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesses the color of the top card, looks at the card, and returns the card to the deck. The player continues to do this, shuffling the deck after each guess.

An online news report claims that 50% of online news readers work in the business industry. To test this claim, a researcher takes an SRS of 25 online news readers. Nine of them work in the business industry. A simulation of 65 trials was conducted under the assumption that 50% of online news readers really do work in the business industry.

Six girls and four boys have entered the science fair. First, second, and third place awards are to be given out.What is the probability that a girl wins the first place award while boys will receive the second and third place awards? Express your answer as a percent.

A lock is opened using a sequence of three numbers. The numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence.What is the probability that all the numbers in the sequence are even? Express your answer as a percent and round to the nearest whole number.

A researcher randomly selects 165 vehicles and sees how many miles each car has been driven and the color of the vehicle. The two-way table displays the data. Suppose a vehicle is randomly selected. Let M = the vehicle has been driven many miles and B = the vehicle is blue.

A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data.Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)?

A landscaper is selecting two trees to plant. He has five to choose from. Three of the five are deciduous and two are evergreen.What is the probability that he chooses trees of two different types? Express your answer as a percent.

The track team gives awards for first, second, and third place runners. There are 10 students from school A and 12 students from school B competing.Which expression represents the probability that all three awards will go to a student from school B?

About 20% of the population experiences "cybersickness.” This happens when the images in 3-D movies look so real they hinder the brain’s ability to sort signals and cause people to get nauseated. To find out if this applies to teens, an SRS of 30 high school students was asked if they experience cybersickness. Eight students said "Yes.” To see if this result is surprising, a simulation is conducted to estimate the probability of obtaining a sample result as high as this.Let 0–1 represent "Yes” and 2–9 represent "No.” Using the line of random numbers, how many "Yes” responses will there be in the first trial of the simulation?